Singular Nature Research Articles

Symbolic equation solving via reinforcement learning

Machine-learning methods are rapidly being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks like simplifying mathematical terms, calculating formal derivatives, or finding exact solutions of algebraic equations. Traditional software packages for these purposes are commonly based on a huge database of rules for how a specific operation (e.g., differentiation) transforms a certain term (e.g., sine function) into another one (e.g., cosine function). These rules have usually needed to be discovered and subsequently programmed by humans. Efforts to automate this process by machine-learning approaches are faced with challenges like the singular nature of solutions to mathematical problems, when approximations are unacceptable, as well as hallucination effects leading to flawed reasoning. We propose a novel deep-learning interface involving a reinforcement-learning agent that operates a symbolic stack calculator to explore mathematical relations. By construction, this system is capable of exact transformations and immune to hallucination. Using the paradigmatic example of solving linear equations in symbolic form, we demonstrate how our reinforcement-learning agent autonomously discovers elementary transformation rules and step-by-step solutions.

Expulsion with no exit: one year of war in Gaza

The first year of war in Gaza has caused the forced displacement of 85% of the population. While it is central to the conflict, little analysis has been conducted from this perspective. The singular nature of this displacement is threefold: the goal of the conflict is expulsion; the purpose of the expulsion is expansion into the territory; and the expulsion is intended to be permanent, with no possibility of return. These three aspects have been a constant in the history of the Palestinian people since the creation of the state of Israel in 1948. Gaza illustrates the calamitous failure of international law, both in the humanitarian field and regarding asylum. What has gone wrong? How do we explain the unjustifiable?

Mass superinflation in the Reissner-Nordström black hole

Ever since Penrose and Simpson's prediction contradicted Novikov's idea that an infalling person would emerge into an asymptotically flat universe, there have been a continued interest in predicting the nature of singularity at the inner horizon of a Reissner-Nordström black hole. This prediction was first confirmed by Poisson and Israel using cross-stream of massless particles, leading to the phenomenon coined as mass inflation. On the other hand, Ori obtained a weaker singularity using a null shell of radiation. Thus it is important to capture the nature of singularity at the inner horizon. We therefore consider in this work a massive scalar field coupled to the Reissner-Nordström spacetime. The ensuing field equations lead to a coupled set of nonlinear dynamical equations. For definiteness, we analytically solve these equations employing the Adomian decomposition method. This facilitates in obtaining a closed form solution that exhibits an unbounded double-exponential growth in the mass function, giving rise to a novel phenomenon coined herein as mass superinflation. The scalar field is also found to undergo a very strong blueshift at the inner horizon.

A Theoretical Perspective on the Stereochemistry of Benzoanellated Aroyl‐X,N‐Ketene Acetal Derivatives

ABSTRACTKetene 1,3‐oxazoles and their derivatives present intriguing structures for the study of rotational barriers due to their pseudo–double‐bond character stemming from resonance in the ketene moiety. A diverse range of compounds featuring this motif underwent quantum‐chemical investigation to elucidate the nature of the stereochemical singularity observed in numerous cases. Because rotational barriers in most instances are too high to permit rapid interconversion, the findings are ascribed to thermodynamic rather than kinetic factors in the gas phase and within an implicit polar medium. The stabilities are attributed to internal hydrogen bonding where feasible. However, in cases where this is not possible, chalcogen bonding rather than steric effects governs the stereochemical preferences, particularly when S and Se comprise the heterocycle of these compounds. These findings hold promise for guiding the design of compounds whose properties hinge on stereochemistry and resonant structures, such as dyes.

Deriving Ritz formulation for the Static Flexural Solutions of Sinusoidal Shear Deformable Beams

This paper presents the Ritz variational method for the static bending analysis of sinusoidal shear deformable beams. The theory accounts for transverse shear deformation and satisfies transverse shear stress-free conditions at the top and bottom surfaces of the beam. The total potential energy functional for the thick beam bending problem is formulated and minimized using a Ritz procedure. The problem considered simply supported boundary conditions and two cases of loading – uniformly distributed load over the span and point load at the center. The function is a function of two unknown displacement functions constructed in terms of unknown generalized displacement parameters and shape functions that satisfy the boundary conditions. Ritz minimization of the functional is used to find the generalized displacement parameters and then the displacements w(x) and The displacements and stresses are found for the loading distributions considered. It is found that the results obtained agree remarkably well with the exact results obtained using the theory of elasticity. The differences between the present results and the exact solutions are less than 0.3% for maximum transverse displacement for both cases of loading considered. For uniform load over the beam, the result for l/t = 10 is 0.112% greater than the exact solution. For the point load at the center, the result for l/t = 10 is 4.468% greater than the exact solution. The increased difference in the point load case is due to the singular nature of the point load problem.

Early-time resonances in the three-dimensional wall-bounded axisymmetric Euler and related equations

We investigate the complex-time analytic structure of solutions of the three-dimensional (3D)-axisymmetric, wall-bounded, incompressible Euler equations, by starting with the initial data proposed in Luo and Hou [“Potentially singular solutions of the 3D axisymmetric Euler equations,” Proc. Natl. Acad. Sci. U. S. A. 111(36), 12968–12973 (2014)], to study a possible finite-time singularity. We use our pseudospectral Fourier–Chebyshev method [Kolluru et al., “Insights from a pseudospectral study of a potentially singular solution of the three-dimensional axisymmetric incompressible Euler equation,” Phys. Rev. E 105(6), 065107 (2022)], with quadruple-precision arithmetic, to compute the time-Taylor-series coefficients of the flow fields, up to a high order. We show that the resulting approximations display early-time resonances; the initial spatial location of these structures is different from that for the tygers, which we have obtained in Kolluru et al. [“Insights from a pseudospectral study of a potentially singular solution of the three-dimensional axisymmetric incompressible Euler equation,” Phys. Rev. E 105(6), 065107 (2022)]. We then perform asymptotic analysis of the Taylor-series coefficients, by using generalized ratio methods, to extract the location and nature of the convergence-limiting singularities and demonstrate that these singularities are distributed around the origin, in the complex-t2 plane, along two curves that resemble the shape of an eye. We obtain similar results for the one-dimensional (1D) wall-approximation (of the full 3D-axisymmetric Euler equation) called the 1D Hou–Luo model, for which we use Fourier-pseudospectral methods to compute the time-Taylor-series coefficients of the flow fields. Our work examines the link between tygers, in Galerkin-truncated pseudospectral studies, and early-time resonances, in truncated time-Taylor expansions of solutions of partial differential equations, such as those we consider.

Social determinants of health and somatic growth in preterm infants and children with chronic lung disease.

Bronchopulmonary dysplasia (BPD), a common complication of prematurity, is associated with impaired lung function and increased morbidity in childhood. These children display heterogeneous somatic growth patterns which may ultimately impact their risk for later respiratory disease. We aim to understand the relationship between socioenvironmental exposures and growth in this population. A retrospective longitudinal cohort study was conducted using participants (n = 616) enrolled in the Johns Hopkins Outpatient BPD Registry. Growth measurements between 0 and 36 months of age were obtained. Somatic growth measurements, both corrected and uncorrected for gestational age, were converted to z-scores using Center for Disease Control and Prevention normative data. Using a participant's residential zip code, we utilized the 2019 Area Deprivation Index (ADI), the Childhood Opportunity Index (COI) 2.0, and neighborhood food insecurity data from the Maryland Food Bank. Linear regression analysis was performed employing individual socioenvironmental measures as independent variables and growth z-scores as dependent variables in univariate analysis. Univariate analysis was repeated adjusting for gestational age, BPD severity, and the presence of a gastrostomy tube (GT). Of the three measures analyzed, national COI (nCOI) showed a significant association with mean weight z-scores, mean ADI showed some association with mean weight z-scores, and the percentage of a community experiencing food insecurity showed no association with mean weight z-scores. After adjusting for gestational age, BPD severity, and presence of a GT, children living in areas of greater opportunity (higher nCOI values), had significantly lower weight z-scores at 12 months corrected and at 24 and 36 months uncorrected CONCLUSIONS: Our findings suggest that the COI 2.0, a multidimensional measure, captures more facets of an individual's social environment, as compared to the singular nature of a measure of food insecurity. There are several potential explanations for the phenomenon seen, and further understanding of this dynamic is crucial for designing effective interventions and policies to better address inequities in outcomes.

Probability And Bayesian Inference In Human Communication

This paper challenges the applicability of traditional information theory's frequentist approach to human communication, arguing that it fails to capture the unique, singular nature of communicative acts. Traditional theory, based on long-term observation and relative frequencies, overlooks the complexity and context-dependency inherent in human interactions. The objective is to redefine communication understanding through a Bayesian model that emphasises subjective probability and the critical role of beliefs and intentions. Utilising a rationalist methodology, the research conducts a qualitative analysis of theoretical concepts and prior research, proposing a new model that situates probability within the philosophy of communication. This model highlights the subjective beliefs and intentions that govern communication, challenging existing paradigms and contributing to a deeper understanding of communicative dynamics. The results reveal the limitations of the frequentist approach and demonstrate the applicability of a Bayesian perspective, advocating for a paradigm shift in communication theory towards a sender-oriented model. This shift not only challenges existing paradigms but also offers a more nuanced understanding of communication as a fundamentally human endeavour.

Integration of Ideological and Political Education in College Physics Courses Under the Reform of Smart Teaching

The development of the times has prompted China to enhance the quality of education and the value of talent. As guides for students, teachers should conscientiously implement ideological and political education, create college physics courses that are more in line with modern talent cultivation, eliminate the fixed and singular nature of traditional teaching, and find the integration points of ideological and political education. Teachers need to use the textbook itself, the expansion of resources in smart classrooms, and current technological progress to implement ideological and political education in order to cultivate more high-quality and high-level comprehensive talents for society.

Testing the weak cosmic censorship conjecture in short haired black holes

The weak cosmic censorship conjecture is a hypothesis about the nature of event horizons and singularities during the formation of black holes. It posits that singularities are always enveloped by the event horizons of black holes, thereby preventing naked singularities from affecting the causal structure of spacetime. In this paper, we study the effect of rotating short haired black holes on the weak cosmic censorship conjecture. Discussion of whether the event horizons of a rotating short haired black hole is disrupted by studying incident neutral test particles and scalar fields. In the context of short haired black holes, when incident neutral test particles are considered for extreme and near extreme cases, our research results indicate that neutral test particles can destroy the event horizons of short haired black holes, violating the weak cosmic censorship conjecture. In the case of scalar field incidence in short haired black holes, for extreme situations, when the incident wave modes fall within the range of 12κM+βMκ<ωm<12Mκ+βMκ-12κ,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{1}{2\\kappa M+\\frac{\\beta }{M\\kappa }}<\\frac{\\omega }{m}<\\frac{1}{2M\\kappa + \\frac{\\beta }{M\\kappa }-\\frac{1}{2\\kappa }},$$\\end{document} the results indicate that the event horizons of rotating short haired black holes is disrupted. For near extreme cases, the presence of hair allows for the disruption of the event horizons of rotating short haired black holes, as indicated by our results. Therefore, these conclusions are intriguing and will provide new insights for us to further understand the weak cosmic censorship conjecture and explore the properties of short haired black holes.

Convergence analysis of a second order numerical scheme for the Flory–Huggins–Cahn–Hilliard–Navier–Stokes system

We present an optimal rate convergence analysis for a second order accurate in time, fully discrete finite difference scheme for the Cahn–Hilliard–Navier–Stokes (CHNS) system, combined with logarithmic Flory–Huggins energy potential. The numerical scheme has been recently proposed, and the positivity-preserving property of the logarithmic arguments, as well as the total energy stability, have been theoretically justified. In this paper, we rigorously prove second order convergence of the proposed numerical scheme, in both time and space. Since the CHNS is a coupled system, the standard ℓ∞(0,T;ℓ2)∩ℓ2(0,T;Hh2) error estimate could not be easily derived, due to the lack of regularity to control the numerical error associated with the coupled terms. Instead, the ℓ∞(0,T;Hh1)∩ℓ2(0,T;Hh3) error analysis for the phase variable and the ℓ∞(0,T;ℓ2) analysis for the velocity vector, which shares the same regularity as the energy estimate, is more suitable to pass through the nonlinear analysis for the error terms associated with the coupled physical process. Furthermore, the highly nonlinear and singular nature of the logarithmic error terms makes the convergence analysis even more challenging, since a uniform distance between the numerical solution and the singular limit values of is needed for the associated error estimate. Many highly non-standard estimates, such as a higher order asymptotic expansion of the numerical solution (up to the third order accuracy in time and fourth order in space), combined with a rough error estimate (to establish the maximum norm bound for the phase variable), as well as a refined error estimate, have to be carried out to conclude the desired convergence result. To our knowledge, it will be the first work to establish an optimal rate convergence estimate for the Cahn–Hilliard–Navier–Stokes system with a singular energy potential.

Comparing sensitivities of groundwater head to variations in hydraulic parameters under boundary conditions of river stage rise and tidal variation

The sensitivity of hydraulic head responses to spatially distributed hydraulic parameters is essential for uncertainty analysis, inverse modeling, and parameter estimation and interpretation. This study formulates the Fréchet sensitivity kernel of hydraulic head responses to a suddenly rising boundary and a sinusoidal head fluctuation boundary to variation of spatially distributed hydraulic parameters in a semi-infinite, one-dimensional (1-D), confined aquifer, and it then derives analytical solutions. Different from previous studies that derived expressions for Fréchet kernels in the time domain for a 2-D pumping test, this study is the first to derive the closed-form Fréchet kernels in time and frequency domains for a semi-infinite, 1-D, confined aquifer. This study uses the Fréchet kernels to investigate the nature of singularities in the spatial sensitivity functions around the observation location and boundary. The information content revealed by observation of head change or head fluctuation amplitude at a given specified location and time (or frequency) under the above two boundary conditions is different. When comparing Fréchet sensitivity kernels across various times or periods, multi-frequency information, much like multi-time information, can be instrumental for hydrogeological parameter inversion. The explicit-form Fréchet sensitivity kernels also identify the optimal time or period for obtaining measurements.

The fractional analysis of thermo-elasticity coupled systems with non-linear and singular nature

It is mentioned that understanding linear and non-linear thermo-elasticity systems is important for understanding temperature, elasticity, stresses, and thermal conductivity. One of the most crucial aspects of the current research is the solution to these systems. The fractional form of several thermo-elastic systems is explored, and elegant solutions are provided. The solutions of fractional and integer thermo-elastic systems are further discussed using tables and diagrams. The closed contact between the LRPSM and exact solutions is displayed in the graphs. Plotting fractional problem solutions demonstrates their convergence towards integer-order problem solutions for suitable modeling. The tables confirm that greater precision is rapidly attained as the terms of the derived series solution increase. The faster convergence and stability of the suggested method support its modification for other fractional non-linear complex systems in nature.

Investigation on the diffusion mechanism of Ga element and regulation of the V-shaped bandgap in CIGS thin films based on magnetron sputtering with a quaternary target

Gradient bandgap engineering has been acknowledged as an effective approach for improving the efficiency of CIGS solar cells. However, an effective method for achieving gradient bandgap engineering in quaternary sputtered CIGS films has not yet been identified.This is due to the uniform and singular nature of the quaternary target composition, as well as the complex kinetic mechanisms that result in the rearrangement of film elements (particularly Ga) during the annealing process. In this study, a grain boundary migration-driven diffusion mechanism for the Ga element in CIGS thin films was established to address the presented issue. The segregation of Ga element is believed to be caused by the flow velocity field generated from the migration of grain boundaries, and the distribution of Ga element can be precisely calculated using the mass transport equation. By modulating the V-shaped bandgap, a notable enhancement in open-circuit voltage (Voc) was achieved, with an increase from 0.405 V to 0.515 V, leading to an effectively improvement of solar cell's efficiency. By comparing and analyzing the actual performance parameters of the solar cells and the simulated results, we conclude that the increase in Voc is due to the alteration in bandgap structure. This study presents a novel approach to bandgap engineering in quaternary sputtered CIGS films through the quantitative calculation of Ga element distribution.

An innovative Fibonacci wavelet collocation method for the numerical approximation of Emden-Fowler equations

This article presents a novel approach using the Fibonacci wavelet collocation method (FWCM) for the numerical solution of Emden-Fowler-type equations. The Emden-Fowler equations are a class of nonlinear differential equations that arise in various fields of science and engineering, particularly in astrophysics and fluid dynamics. Due to their nonlinear and singular nature, the conventional approaches to solving these equations encounter difficulties. This method is particularly effective in handling problems with singularities, as it adapts naturally to the local behaviour of the solution. Here, we introduced the Fibonacci wavelet collocation method as a powerful numerical technique for tackling Emden-Fowler-type equations. The Fibonacci wavelet basis functions possess remarkable properties, including compact support, making them well-suited for approximating solutions to differential equations. The main advantage of this approach lies in its ability to reduce the computational complexity associated with solving Emden-Fowler equations, resulting in accurate and efficient solutions. Comparative analyses with other established numerical methods reveal its superior accuracy and convergence rate performance. Further, several examples demonstrate the method's flexibility when dealing with different singularity levels. This paper contributes to numerical analysis by introducing the Fibonacci wavelet method as a robust tool for solving Emden-Fowler-type equations.

Genomic, functional, and metabolic enhancements in multidrug-resistant Enterobacter bugandensis facilitating its persistence and succession in the International Space Station

BackgroundThe International Space Station (ISS) stands as a testament to human achievement in space exploration. Despite its highly controlled environment, characterised by microgravity, increased CO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{2}$$\\end{document} levels, and elevated solar radiation, microorganisms occupy a unique niche. These microbial inhabitants play a significant role in influencing the health and well-being of astronauts on board. One microorganism of particular interest in our study is Enterobacter bugandensis, primarily found in clinical specimens including the human gastrointestinal tract, and also reported to possess pathogenic traits, leading to a plethora of infections.ResultsDistinct from their Earth counterparts, ISS E. bugandensis strains have exhibited resistance mechanisms that categorise them within the ESKAPE pathogen group, a collection of pathogens recognised for their formidable resistance to antimicrobial treatments. During the 2-year Microbial Tracking 1 mission, 13 strains of multidrug-resistant E. bugandensis were isolated from various locations within the ISS. We have carried out a comprehensive study to understand the genomic intricacies of ISS-derived E. bugandensis in comparison to terrestrial strains, with a keen focus on those associated with clinical infections. We unravel the evolutionary trajectories of pivotal genes, especially those contributing to functional adaptations and potential antimicrobial resistance. A hypothesis central to our study was that the singular nature of the stresses of the space environment, distinct from any on Earth, could be driving these genomic adaptations. Extending our investigation, we meticulously mapped the prevalence and distribution of E. bugandensis across the ISS over time. This temporal analysis provided insights into the persistence, succession, and potential patterns of colonisation of E. bugandensis in space. Furthermore, by leveraging advanced analytical techniques, including metabolic modelling, we delved into the coexisting microbial communities alongside E. bugandensis in the ISS across multiple missions and spatial locations. This exploration revealed intricate microbial interactions, offering a window into the microbial ecosystem dynamics within the ISS.ConclusionsOur comprehensive analysis illuminated not only the ways these interactions sculpt microbial diversity but also the factors that might contribute to the potential dominance and succession of E. bugandensis within the ISS environment. The implications of these findings are twofold. Firstly, they shed light on microbial behaviour, adaptation, and evolution in extreme, isolated environments. Secondly, they underscore the need for robust preventive measures, ensuring the health and safety of astronauts by mitigating risks associated with potential pathogenic threats.DtSaop7bYTNkSCdR7trwLeVideo

It is Not Too Late for Reconciliation Between Israel and Palestine, Even in the Darkest Hour

The conflict in Gaza and Israel that ignited on October 7, 2023 signals a catastrophic breakdown in the possibility of ethical dialogue in the region. The actions on both sides have revealed a dissolution of ethical restraints, with unimaginably cruel attacks on civilians, murder of children, destruction of health facilities, and denial of basic needs such as water, food, and shelter. There is a need both to understand the nature of the ethical singularity represented by this conflict and what, if any, options are available to allow the reconstruction of communication between the warring parties. This article seeks to address these tasks by analysing the conflict as inherently an ethical one, in the sense that it exposes a rupture in the fabric of communicative relationships that has evolved systematically out of the deep cultural structures from which all protagonists have emerged. Drawing on the work of Levinas, Habermas, Arendt, and others, and referring to the specific circumstances in the region, it examines the ethical sources of the crisis and tries to identify conditions for its resolution. The possibility of reconciliation—that is, of refiguring relationships to open up a space for dialogue to create pathways to heal the ruptures—is examined. The dark legacy of the Holocaust is identified as an abiding cultural vulnerability for both societies. It is concluded, however, that the rich history of partnerships and collaborations between Jews and Palestinians provides a robust infrastructure on the basis of which a sustainable peace might be built, providing a much-needed source of hope.

Gravitational collapse in energy-momentum squared gravity: Nature of singularities

In this paper we explore a collapsing scenario in the background of energy-momentum squared gravity (EMSG). EMSG claims to have terms that originate from the quantum gravity effects mimicking loop quantum gravity. As a result the framework admits a bounce at a finite time thus avoiding a singularity. So the question that naturally arises: Is there any realistic chance of formation of a black hole or the quantum gravity effects are strong enough to totally avoid such a pathology? Motivated from this we are interested in studying a gravitational collapse mechanism in the background of EMSG and investigate the fate of such a process. We model the spacetime of a massive star by the Vaidya metric and derive the field equations in EMSG. Then using the equations we go on to study a gravitational collapse mechanism, on two specific models of EMSG with different forms of curvature-matter coupling. The prime objective is to probe the nature of singularity (if formed) as the end state of the collapse. We see that none of the models generically admit the formation of black holes as the end state of collapse, but on the contrary they support the formation of naked singularities. This can be attributed to the quantum fluctuations of the gravitational interactions at the fundamental level.

A Guide to Cross-Sectional Studies in Homeopathic Research: Part 3 of the Research Method Series

AbstractThe cross-sectional study design, a prominent feature in the realm of health research, entails the simultaneous measurement of outcomes and exposures among study participants. This study design finds frequent application in homeopathic contexts, particularly in population-based surveys and the evaluation of disease prevalence or understanding the patient preferences in clinic-based samples. Notably, the utilisation of cross-sectional studies in homeopathy brings forth advantages such as expeditiousness and cost-effectiveness. These studies, serving as valuable precursors, play a pivotal role in offering crucial information before embarking on more extensive research endeavours, such as planning comprehensive cohort studies or establishing baseline measurements. While their rapid and economical nature allows for the efficient assessment of prevalence and associations, it is imperative to exercise caution when drawing causal inferences, given the singular nature of exposure and outcome measurements. This paper is meticulously designed to serve as a guide, aiding readers in comprehending the intricate nuances of cross-sectional study design and their judicious application in real-world scenarios, particularly within the dynamic landscape of homeopathy. By delving into the deeper aspects of conducting and reporting such studies, this paper aims to equip researchers and practitioners with the knowledge and insights needed to navigate the technicalities of cross-sectional research within the distinctive context of homeopathic practice.

Lafza ('af) in The Holly Qur’an: An Analytical Study

ABSTRACT This study highlights the significance of language and its influence on the human psyche. It underscores the importance of respecting parents and refraining from using derogatory language towards them. The term "f" encompasses various negative connotations, thus it serves as a warning against verbal abuse towards parents. It is imperative to show reverence towards parents and avoid causing them any offense. This study affirms the significance of each word in the Holy Qur’an. Specifically, the verses in Surat al-Isra’ and al-Ahqaf that mention the word “f” highlight the potential consequences of disrespecting one's parents, which is considered a major sin requiring repentance for forgiveness. The use of the small word “f” serves as evidence of disobedience towards parents and may lead to punishment in the afterlife. The research revealed that the letter "F" in Surat Al-Anbiya signifies the significant historical event of disproving the divinity of idols during the time of Prophet Abraham. This event emphasizes the belief in the singular and supreme nature of God. The word "F" represents the courage displayed by Prophet Ibrahim in confronting the oppressive leaders of his community.